<?php
/**
 * @title 410. 分割数组的最大值 - 动态规划
 * @author start2004
 */

class Solution {

    /**
     * @param Integer[] $nums
     * @param Integer $m
     * @return Integer
     */
    function splitArray($nums, $m) {
        /**
         * @since 2021-08-23 长度
         */
        $len = count($nums);

        /**
         * @since 2021-08-23 dpArray(i, j)表示前i个数分成j段数组和最大值的最小
         */
        $dpArray = [];
        $dpArray[0][0] = 0;

        /**
         * @since 2021-08-23 sub(k+1, i)表示从k+1到i位子数组之和
         * @since 2021-08-23 sumArray(n)表示前n个数之和
         * @since 2021-08-23 sub(k+1,i)=sumArray(i)−sumArray(k)
         */
        $sumArray = [0];
        for($i=1; $i<=$len; $i++){
            $sumArray[$i] = $sumArray[$i-1] + $nums[$i-1];

            /**
             * @since 2021-08-24 只分一个组
             */
            $dpArray[$i][1] = $sumArray[$i];
            $dpArray[$i][0] = 0;
        }
        // var_dump($dpArray);

        /**
         * @since 2021-08-24 查找子数组和最大值的最小值
         */
        for ($i=1; $i<=$len; $i++){
            for($j=2; $j<=min($i, $m); $j++){
                // echo "i={$i}, j={$j}", PHP_EOL;

                $sumMin = PHP_INT_MAX;
                for($k=$j-1; $k<=$i-1; $k++){
                    $sumMax = max($dpArray[$k][$j-1], $sumArray[$i]-$sumArray[$k]);
                    $sumMin = min($sumMin, $sumMax);
                    // echo "k={$k}, sumMax={$sumMax}", PHP_EOL;
                }
                // echo "sumMin={$sumMin}", PHP_EOL, PHP_EOL;
                $dpArray[$i][$j] = $sumMin;
            }
        }
        // var_dump($dpArray);

        /**
         * @return
         */
        return $dpArray[$len][$m];
    }
}




/**
 * @url http://127.0.0.1/leetcode/202007/2020.07.25_3.php
 */
$datas = [
    // [[1,60,25,25,1,1], 4], //
    [[1,60,25,25,1,1,30,110,40,70,37], 4], // 140
    [[5,2,4,1,3,6,0], 2], // 11
    [[3,2,3,1,2,4,1,1,10,11,2], 8], // 11
    [[3,2,3,1,2,4,5,5,6,7,7,8,2,3,1,1,1,10,11,5,6,2,4,7,8,5,6], 20], // 11
    [[7,2,5,10,8], 5], // 10
    [[7,2,5,10,8], 2], // 18
    [[5334,6299,4199,9663,8945,3566,9509,3124,6026,6250,7475,5420,9201,9501,38,5897,4411,6638,9845,161,9563,8854,3731,5564,5331,4294,3275,1972,1521,2377,3701,6462,6778,187,9778,758,550,7510,6225,8691,3666,4622,9722,8011,7247,575,5431,4777,4032,8682,5888,8047,3562,9462,6501,7855,505,4675,6973,493,1374,3227,1244,7364,2298,3244,8627,5102,6375,8653,1820,3857,7195,7830,4461,7821,5037,2918,4279,2791,1500,9858,6915,5156,970,1471,5296,1688,578,7266,4182,1430,4985,5730,7941,3880,607,8776,1348,2974,1094,6733,5177,4975,5421,8190,8255,9112,8651,2797,335,8677,3754,893,1818,8479,5875,1695,8295,7993,7037,8546,7906,4102,7279,1407,2462,4425,2148,2925,3903,5447,5893,3534,3663,8307,8679,8474,1202,3474,2961,1149,7451,4279,7875,5692,6186,8109,7763,7798,2250,2969,7974,9781,7741,4914,5446,1861,8914,2544,5683,8952,6745,4870,1848,7887,6448,7873,128,3281,794,1965,7036,8094,1211,9450,6981,4244,2418,8610,8681,2402,2904,7712,3252,5029,3004,5526,6965,8866,2764,600,631,9075,2631,3411,2737,2328,652,494,6556,9391,4517,8934,8892,4561,9331,1386,4636,9627,5435,9272,110,413,9706,5470,5008,1706,7045,9648,7505,6968,7509,3120,7869,6776,6434,7994,5441,288,492,1617,3274,7019,5575,6664,6056,7069,1996,9581,3103,9266,2554,7471,4251,4320,4749,649,2617,3018,4332,415,2243,1924,69,5902,3602,2925,6542,345,4657,9034,8977,6799,8397,1187,3678,4921,6518,851,6941,6920,259,4503,2637,7438,3893,5042,8552,6661,5043,9555,9095,4123,142,1446,8047,6234,1199,8848,5656,1910,3430,2843,8043,9156,7838,2332,9634,2410,2958,3431,4270,1420,4227,7712,6648,1607,1575,3741,1493,7770,3018,5398,6215,8601,6244,7551,2587,2254,3607,1147,5184,9173,8680,8610,1597,1763,7914,3441,7006,1318,7044,7267,8206,9684,4814,9748,4497,2239],9], // 194890
];

include_once dirname(__DIR__) . DIRECTORY_SEPARATOR ."xhprof.php";
$xhprof = new Xhprof();
foreach ($datas as $data){
    // var_dump($data);

    $obj = new Solution();
    $result = $obj->splitArray($data[0], $data[1]);
    var_dump($result);
    echo str_repeat("<br>", 3);
}
$xhprof->end();
